A264024 a(n) = gcd(phi(k), k-1) / lambda(k), where k is n-th Carmichael number A002997(n) and lambda(k) = A002322(k).

1, 1, 12, 2, 1, 1, 9, 1, 4, 1, 6, 18, 1, 1, 1, 2, 1, 1, 1, 2, 12, 1, 1, 1, 1, 3, 3, 3, 50, 1, 18, 2, 1, 2, 1, 2, 5, 36, 1, 1, 2, 3, 4, 3, 3, 2, 3, 1, 1, 3, 3, 2, 4, 2, 5, 1, 4, 4, 4, 1, 1, 3, 40, 28, 1, 2, 4, 2, 4, 1, 2, 1, 2, 1, 33, 5, 50, 64, 1, 1, 3, 2, 1, 1, 12, 3, 1, 12, 1, 1, 1, 24, 1, 3, 128, 1, 6, 8, 5, 20, 3, 2, 2, 6, 4

Offset: 1

Author

Thomas Ordowski, Nov 01 2015

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002322, A002997, A049559, A174590, A264012.

Programs

Mathematica

t = Cases[Range[1, 16 (10^6), 2], n_ /; Mod[n, CarmichaelLambda@ n] == 1 && ! PrimeQ@ n]; Table[GCD[EulerPhi@ t[[n]], t[[n]] - 1]/CarmichaelLambda@ t[[n]], {n, 105}] (* Michael De Vlieger, Nov 03 2015, after Artur Jasinski at A002997: alternatively use A002997 data for t *)

PARI

t(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;
is(n)=n%2 && !isprime(n) && t(n) && n>1;
c(n)=gcd(eulerphi(n),n-1)/lcm(znstar(n)[2]);
for(n=1, 1e7, if(is(n), print1(c(n)", "))) \\ Altug Alkan, Nov 01 2015

Formula

a(n) = A049559(k)/A002322(k), where k = A002997(n).

Extensions

More terms from Altug Alkan, Nov 01 2015